Multidimensional coded modulation for wireless communications with physical layer security

ABSTRACT

Systems and methods for quantum key distribution using orbital angular momentum (OAM)-modes-enabled secure multidimensional coded modulation. The quantum key distribution including symbols of a raw key across subcarriers and multiplexing the subcarriers to form an electrical carrier. Then optically modulating the electrical carrier with an electro-optical modulator using an optical signal. The optically modulated electrical carrier is then imposed on a pre-determined OAM mode using an optical OAM multiplexer, attenuated, and transmitted across a quantum channel. A receiver then receives the transmitted signal and demultiplexes it with an optical OAM demultiplexer to extract projections. The projections then undergo optical-to-electrical conversion using a coherent optical detector with an optical signal from a local oscillator. A resulting estimated electrical carrier is then demultiplexed into subcarriers. The subcarrier undergo phase noise cancellation and subsequent demodulation to extract estimated symbol constellation points corresponding the symbols of the raw key.

RELATED APPLICATION INFORMATION

This application claims priority to 62/459,688, filed on Feb. 16, 2017,incorporated herein by reference in its entirety. This application isrelated to U.S. Utility Application No. 15/897,913 filed Feb. 15, 2018entitled “ANTENNA ARRAY BASED OAM WIRELESS COMMUNICATION”, and U.S.Utility Application No. 15/897,944 filed Feb. 15, 2018 entitled“MULTIDIMENSIONAL CODED MODULATION FOR WIRELESS COMMUNICATIONS”, andwhich are incorporated by reference herein in their entirety.

BACKGROUND Technical Field

The present invention relates to wireless communication and moreparticularly to wireless communications using orbital angular momentumwith multidimensional coded modulation.

Description of the Related Art

In wireless communication and telecommunications, signals arecommunicated between transmitter and receiver by modulating a radiofrequency (RF) signal. By multiplexing a RF signal over one or moredegrees of freedom (DOF), multiple signals may be sent at the same time.Thus, multiplexing of signals effectively increases the aggregatethroughput of a network.

However, as more and more bandwidth is demanded for wirelesscommunication, the upper limits of currently implemented DOFs becomerestricting. These restrictions on bandwidth limitation, not only thespeed and capacity of a network, but also the security of and the energyused by the wireless signals.

SUMMARY

According to an aspect of the present principles, a method is providedfor quantum key distribution using orbital angular momentum(OAM)-modes-enabled secure multidimensional coded modulation. Thequantum key distribution includes modulating sequences at a transmitter,each of the sequences including at least one symbol of a raw key, togenerate subcarriers corresponding to the sequences. The subcarriers arethen subcarrier multiplexed into at least one electrical carrier signal,which is optically modulated via electro-optical modulation with anelectro-optical modulator, into at least one optical carrier generatedby an optical source. The electro-optical modulation includes imposingeach of the optical carriers on a pre-determined optical OAM mode, usingan optical OAM multiplexer configured to shift an azimuthal phase termof the transmitter corresponding to each of the pre-determined opticalOAM modes, to produce an optical OAM supercarrier containing each of theoptical carriers in a corresponding orthogonal OAM mode. The methodfurther includes attenuating the optical OAM supercarrier down to a shotnoise level range with an optical attenuator and communicating theoptical OAM supercarrier across a quantum optical wireless communicationchannel. The method includes demultiplexing the optical OAMsupercarrier, at a receiver, to extract projections corresponding toestimated optical carriers by shifting an azimuthal phase term of thereceiver corresponding to each of the pre-determine optical OAM modes. Acoherent optical detector is then used to perform optical-to-electricalconversion on the estimated optical carriers using an OAM projectedsignal, and a signal from a local oscillator to generate estimatedelectrical carrier signals. The estimated electrical carrier signalswill then undergo subcarrier demultiplexing into multiple estimatedsubcarriers. The method further includes phase noise cancelling, at aphase noise cancellation (PNC) stage, each of the plurality ofsubcarriers to remove laser phase noise and random phase shifts from theplurality of estimated subcarriers. Demodulating the estimatedsubcarriers is then performed to extract corresponding estimated symbolconstellation points corresponding to the raw key.

According to another aspect of the present principles, a transmitter isprovided for quantum key distribution using orbital angular momentum(OAM)-modes-enabled secure multidimensional coded modulation. Thetransmitter includes at least one multidimensional modulation systemincluding a subcarrier multiplexing system configured to multiplexmultidimensional signals, each of the multidimensional signals includingat least one sequence of a raw key, to generate subcarrierscorresponding to the sequences, and multiplex the subcarriers into atleast one electrical carrier signal. An electro-optical modulator isemployed and configured to modulate the at least one electrical carriersignal via electro-optical modulation with an electro-optical modulator,into at least one optical carrier generated by an optical source. Theelectro-optical modulation includes imposing each of the at least oneoptical carrier on a pre-detennined optical OAM mode, using an opticalOAM multiplexer including computer generated holograms, to produce anoptical OAM supercarrier containing each of the at least one opticalcarriers in a corresponding orthogonal OAM mode. An optical attenuatoris employed and configured to attenuate the optical OAM supercarrierdown to a shot noise level range and transmit the attenuated OAMsupercarrier over a quantum channel.

According to another aspect of the present principles, a receiver isprovided for quantum key distribution using orbital angular momentum(OAM)-modes-enabled secure multidimensional coded modulation. Thereceiver includes an optical OAM demultiplexer configured to perform OAMdemultiplexing of an optical OAM supercarrier to extract projectionscorresponding to at least one estimated optical carrier usingcomplex-conjugate shifting of an azimuthal phase term of the receivercorresponding to pre-determined optical OAM modes. A coherent opticaldetector is employed and configured to combine, with an optical hybrid,the projections with a laser signal from a local oscillator, performbalanced photodetection for optical-to-electrical conversion, todetermine an optically detected subcarrier multidimensional signal. Asubcarrier demultiplexer is used to subcarrier demultiplex thecorresponding optically detected subcarrier multidimensional signal intomultidimensional subcarriers. At least one phase noise cancellation(PNC) device will phase noise cancel each of the subcarriers to removelaser phase noise and random phase shifts from the estimatedsubcarriers. A multidimensional demodulator corresponding to each ofestimated subcarriers is used to demodulate estimated sequences ofsymbol constellation points corresponding to the raw key.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 is a block/flow diagram illustrating a high-level system/methodfor wireless communication with orbital angular momentum(OAM)-modes-enabled secure multidimensional coded modulation, inaccordance with the present principles;

FIG. 2 is a block/flow diagram illustrating a system/method for atransmitter and antenna array element for wireless communication withOAM-modes-enabled secure multidimensional coded modulation, inaccordance with the present principles;

FIG. 3 is a flow diagram illustrating a system/method for a receiver forwireless communication with OAM-modes-enabled secure multidimensionalcoded modulation, in accordance with the present principles;

FIG. 4 is a block/flow diagram illustrating a system/method for anencryption scheme for a wireless communication with OAM-modes-enabledsecure multidimensional coded modulation, in accordance with the presentprinciples;

FIG. 5 is a block/flow diagram illustrating a system/method for amasking scheme for a wireless communication with OAM-modes-enabledsecure multidimensional coded modulation, in accordance with the presentprinciples;

FIG. 6 is a block/flow diagram illustrating a system/method for anantenna array configuration for OAM multiplexing and demultiplexing, inaccordance with the present principles;

FIG. 7 is a block/flow diagram illustrating a system/method for a2L-dimensional modulator for wireless communication withOAM-modes-enabled secure multidimensional coded modulation, inaccordance with the present principles;

FIG. 8 is a block/flow diagram illustrating a system/method for a2L-dimensional demodulator for wireless communication withOAM-modes-enabled secure multidimensional coded modulation, inaccordance with the present principles;

FIG. 9 is a block/flow diagram illustrating a system/method for a coded2L-dimensional modulator for wireless communication withOAM-modes-enabled secure multidimensional coded modulation, inaccordance with the present principles;

FIG. 10 is a block/flow diagram illustrating a system/method for an2L-dimensional iterative demapper and decoder for wireless communicationwith OAM-modes-enabled secure multidimensional coded modulation, inaccordance with the present principles;

FIG. 11 is a block/flow diagram illustrating a system/method forunconditional physical layer security with optical wirelesscommunication with OAM-modes-enabled secure multidimensional codedmodulation, in accordance with the present principles;

FIG. 12 is a block/flow diagram illustrating a system/method forwireless transmission with OAM-modes-enabled secure multidimensionalcoded modulation, in accordance with the present principles;

FIG. 13 is a block/flow diagram illustrating a system/method forreceiving a wireless signal with OAM-modes-enabled securemultidimensional coded modulation is illustratively depicted inaccordance with one embodiment of the present principles;

FIG. 14 is a block/flow diagram illustrating a system/method forwireless transmission with multidimensional coded modulation usingbaseband functions, in accordance with the present principles;

FIG. 15 is a block/flow diagram illustrating a system/method forreceiving a wireless signals for multidimensional coded modulation usingbaseband functions, in accordance with one embodiment of the presentprinciples;

FIG. 16 is a block/flow diagram illustrating a system/method forunconditional physical layer security for optical wireless communicationwith OAM-modes-enabled secure multidimensional coded modulation, inaccordance with the present principles.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In accordance with the present principles, systems and methods areprovided for wireless communication with orbital angular moment (OAM)based, secured, energy-efficient multidimensional coded modulation.

In one embodiment, challenges related to a higher bandwidthinfrastructure are contemplated. As wireless communications demandgreater bandwidth, infrastructure capacity must grow to accommodate thatdemand. One way of increasing the capacity of the infrastructure toaccommodate increased bandwidth is by introducing another degree offreedom to a wireless link. More degrees of freedom in a wireless linkpermit a higher dimensional space for coding symbols to a signalconstellation space by increasing the number of dimensions correspondingto the signal constellation space. Such an additional degree of freedommay include the orbital angular momentum (OAM) of a radio frequency (RF)signal.

By introducing OAM as a degree of freedom for signal transmission,signals may be multiplexed across RF channels such as an in-phasechannel and a quadrature channel, as well as polarization states, and adesired number of OAM modes. Accordingly, a symbol can be coded to asignal constellation point in a relatively large constellation spaceincluding at least the above mentioned degrees of freedom. The highdimensional constellation space increases the amount of information thatcan be coded to the space, as well as increasing the accuracy ofencoding and decoding the signal constellation point.

As a result, greater spectral efficiency, energy efficiency and securityare contemplated by increasing the dimensionality of RF signals inwireless links, such as with the addition degrees of freedomcorresponding to OAM modes. Thus, improved wireless communicationsutilizing OAM mode based wireless communication may be used for currentand future wireless standards, such as 2G, 3G, 4G, 5G and beyond, aswell as any other wireless communication standard.

Embodiments described herein may be entirely hardware, entirely softwareor including both hardware and software elements. In a preferredembodiment, the present invention is implemented in software, whichincludes but is not limited to firmware, resident software, microcode,etc.

Embodiments may include a computer program product accessible from acomputer-usable or computer-readable medium providing program code foruse by or in connection with a computer or any instruction executionsystem. A computer-usable or computer readable medium may include anyapparatus that stores, communicates, propagates, or transports theprogram for use by or in connection with the instruction executionsystem, apparatus, or device. The medium can be magnetic, optical,electronic, electromagnetic, infrared, or semiconductor system (orapparatus or device) or a propagation medium. The medium may include acomputer-readable storage medium such as a semiconductor or solid statememory, magnetic tape, a removable computer diskette, a random accessmemory (RAM), a read-only memory (ROM), a rigid magnetic disk and anoptical disk, etc.

Each computer program may be tangibly stored in a machine-readablestorage media or device (e.g., program memory or magnetic disk) readableby a general or special purpose programmable computer, for configuringand controlling operation of a computer when the storage media or deviceis read by the computer to perform the procedures described herein. Theinventive system may also be considered to be embodied in acomputer-readable storage medium, configured with a computer program,where the storage medium so configured causes a computer to operate in aspecific and predefined manner to perform the functions describedherein.

A data processing system suitable for storing and/or executing programcode may include at least one processor coupled directly or indirectlyto memory elements through a system bus. The memory elements can includelocal memory employed during actual execution of the program code, bulkstorage, and cache memories which provide temporary storage of at leastsome program code to reduce the number of times code is retrieved frombulk storage during execution. Input/output or I/O devices (includingbut not limited to keyboards, displays, pointing devices, etc.) may becoupled to the system either directly or through intervening I/Ocontrollers.

Network adapters may also be coupled to the system to enable the dataprocessing system to become coupled to other data processing systems orremote printers or storage devices through intervening private or publicnetworks. Modems, cable modem and Ethernet cards are just a few of thecurrently available types of network adapters.

Referring now in detail to the figures in which like numerals representthe same or similar elements and initially to FIG. 1, a high-levelsystem/method for wireless communication with OAM-modes-enabled securemultidimensional coded modulation is illustratively depicted inaccordance with one embodiment of the present principles.

In one embodiment, included in a system for wireless communication is awireless communication device 1. Wireless communication device 1 mayinclude, e.g., a transmitter and/or receiver in communication with anantenna or antenna array for transmitting and/or receivingelectromagnetic (EM) signals. Such EM signals may include, e.g., radiofrequency (RF) signals, millimeter wave signals, terahertz (THz)signals, free-space optical (FSO) signals, or any other EM signalsuitable for carrying information.

The wireless communication device 1 may be in communication with a datasource 3 such as, e.g., a server or cloud server, a cloud computingsystem, data center, a virtual machine, a computer, or anything othersuitable data device. The data source 3 provides the wirelesscommunication device 1 with the signal to be transmitted. Alternatively,or in addition, the data source 3 may be a destination for a signalreceived by the wireless communication device 1. The data source 3 maybe in communication with the wireless communication device 1 via awireless connection, such as, e.g., RF or millimeter way, or FSO, orothers, or by a wired connection, such as, e.g., copper wire, fiber,coaxial cables, superconductor connections, or any other connectionsuitable for carrying signals.

The wireless communication device 1 may then communicate the signal withother devices capable of communicating a corresponding wireless device,such as an antenna or antenna array. The other devices may include, forexample, a router 2 a, a smartphone or other mobile device 2 b, apersonal computer 2 c, a server 2 d or a database 2 e, and any otherdevice capable of communication via EM waves. As such, devices 2 a-2 emay include wireless communication devices similar to the wirelesscommunication device 1, including, e.g., a transmitter and/or receiverin communication with an antenna or antenna array, such that the devices2 a-2 e may wireless communication with the wireless communicationdevice 1.

To permit communication with devices 2 a-2 e, the wireless communicationdevice 1 may encode a signal according to aspects of the presentinvention. Accordingly, the wireless communication device 1 may encodethe signal by leveraging all available degrees of freedom, includingorbital angular momentum (OAM) of the EM wave being transmitted. The EMwave may be in the RF domain in which the signal is encoded using amultidimensional coded modulation scheme. The multidimensional codedmodulation scheme may include multiplexing across an in-phase channel, aquadrature channel, passbands, polarization states and/or OAM modes.Accordingly, the signal may be multiplexed in a very large dimensionalspace including a combination of any of the above degrees of freedom. Aswill be described below, such a multiplexing scheme increases thespectral efficiency with greater tolerance to fading, multipath,interference effects, nonlinearities and other wireless transmissionimpairments.

Additionally, by multiplexing the signal with the wireless communicationdevice 1 across more degrees of freedom with higher dimensionality,aggregate secrecy capacity may also be dramatically improved.Accordingly, as will be described below, wireless encryption schemesbased on the greater degrees of freedom are possible for more securesignal encryption.

Furthermore, the increased degrees of freedom and higher dimensionalityof the transmission from the wireless signal device 1 may permitimproved physical-layer security at the wireless communication device 1and/or the devices 2 a-2 e. For example, to provide unconditionalsecurity, subcarrier multiplexing based continuous variable quantum keydistribution (CV-QKD) with reverse reconciliation over optical wirelesscommunication (OWC) links may leverage degrees of freedom such as, e.g.,OAM modes, to improve secrecy capacity, bit error rate and secure keyrates. These principles may also be applied to classical andsemi-classical physical layer security schemes. Accordingly, as will bedescribed below, the wireless communication device 1 and devices 2 a-2 emay have improved physical-layer security.

As another example, physical-layer security may be implemented in aflood-light quantum key distribution (FL-QKD). In FL-QKD, a transmittermay include a broadband amplified spontaneous emission (ASE) lightsource to generate correlated reference and signal light. An intendedreceiver employs the ASE non-modulated signal, modulates it, and sendsit back as a returned message to the original transmitter. The otherside may then employ a homodyne receiver to decode the returned message.A photon-pair source and three single-photon detectors (SPDs) are usedto monitor an intruder attempting to intercept the returned message. Byemploying a microwave illumination approach, a mm-wave, THz wave or RFwave can be entangled with an optical beam. Employing FL-QKD withmicrowave illumination multi-Gb/s secure key rates over mm-wave/THz/RFlinks can be achieved. In this scenario, the weak optical beam is usedto monitor the intruder, while mm-wave/THz/RF link is used for raw-keytransmission.

The wireless communication device 1 may implement greater degrees offreedom by, for example, multiplexing across OAM modes. OAM modesleverage a helical wavefront, such as a Laguerre-Gaussian (LG) vortexbeam, produced by an antenna or antenna array to generate a nonzeroangular momentum J, according to equation 1 below:

$\begin{matrix}{{J = {{\frac{1}{4\pi\; c}{\int_{V}{E \times {AdV}}}} + {\frac{1}{4\pi\; c}{\int_{V}{\sum\limits_{{k = x},y,z}{\left( {r \times \nabla} \right)A_{k}\ {dV}}}}}}},} & {{Equation}\mspace{14mu} 1}\end{matrix}$

where J is the angular momentum of an electromagnetic (EM) field, c isthe speed of light, E is the electric field intensity, A is the vectorpotential, r is the radius of the EM field, ∇ is the del operator, and Vis the volume in which propagation is observed.

The vector potential, A, of a vortex beam imposed by a circulartraveling-wave antenna or circular array antenna may be determined basedon equation 2 below;

$\begin{matrix}{{{A(r)} = {{\frac{\mu_{0}I_{0}}{4\pi}{\int_{L}{e^{{jl}\;\phi}\frac{e^{{jk}{{r - r^{\prime}}}}}{{r - r^{\prime}}}\ {dl}^{\prime}}}} \cong {{\frac{\left( {- j} \right)^{- 1}a}{r}\frac{\mu_{0}I_{0}e^{jkr}}{4}e^{{jl}\;\phi}{{J_{l - 1}\left( {{ka}\mspace{14mu}\sin\mspace{14mu}\theta} \right)}\left\lbrack {{\sin\mspace{14mu}\theta\mspace{14mu}\hat{r}} + {\cos\mspace{14mu}\theta\mspace{14mu}\hat{\theta}} + {j\;\hat{\phi}}} \right\rbrack}} + {\frac{\left( {- j} \right)^{- 1}a}{r}\frac{\mu_{0}I_{0}e^{jkr}}{4}e^{{jl}\;\phi}{{J_{l - 1}\left( {{ka}\mspace{14mu}\sin\mspace{14mu}\theta} \right)}\left\lbrack {{\sin\mspace{14mu}\theta\mspace{14mu}\hat{r}} + {\cos\mspace{14mu}\theta\mspace{14mu}\hat{\theta}} - {j\;\hat{\phi}}} \right\rbrack}}}}},} & {{Equation}\mspace{14mu} 2}\end{matrix}$

where e^(jlϕ) corresponds to the azimuthal phase dependence of the l-thOAM mode of the vector potential, a is the radius of a circular antenna,μ is the free space permeability, k is the propagation constant equal to2π/λ where λ is the wavelength, and θ and ϕ are spherical coordinates.

For optical wireless communication (OWC), including outdoor FSO links,the LG(p,m) beams can be used. Given that an LG beam has both a radialmode p and an angular mode m, the radial mode p may be held constant dueto rotational symmetry, thus resulting in all OAM modes m being mutuallyorthogonal.

For circular antenna arrays and circular-traveling wave antennas,equation 2 may be substituted into equation 1, resulting in equation 3below:L _(z)=ε₀∫₀ ^(2π) dϕ∫∫Re{jE*({circumflex over (L)}·A)}ρdρdz,{circumflexover (L)}=−j(r×∇),  Equation 3:

where {circumflex over (L)} is the angular momentum operator, Reindicates real component of a complex number, j is the imaginary unit,and ρ and z are cylindrical coordinates.

As a result of the above, a suitable antenna or antenna array, such as,e.g., a circular traveling-wave antenna, a spiral parabolic antenna, ora dual mode antenna may be used to generate an RF carrier wave having adesired angular momentum. For example, by using a circular antenna arrayas the wireless communication device 1, the circular antenna may bedivided into N segments, with each segment having an incremental phaseshift of 2πl/N, with l corresponding to a desired angular OAM mode.Accordingly, the same RF signal may be produced at each segment, butwith a different one of the l OAM modes. Accordingly, the wirelesscommunication device 1 may be used to generate a signal multiplexedacross OAM modes.

OAM antenna array may be used in the wireless communication device 1,such as, e.g., a circular antenna array, described above, or linearantenna array. In the antenna array, an antenna array element produces acorresponding electric field characterized by equation 4 below:

$\begin{matrix}{{E_{0} = {\frac{I_{0}}{4\pi}\frac{e^{- {jkr}}}{r}}},} & {{Equation}\mspace{14mu} 4}\end{matrix}$

where E₀ is the electrical field for far field, I₀ is the currentmagnitude applied to the antenna array, j is the imaginary unit, k isthe wave number, and r is the distance from the origin. For a linearantenna array, placed along z-axis, having (2N+1) linear elements, thedistances of observed point in far-field from the array elements aredefined by r±nd cos θ where n is the array element index (n=−N, . . . ,−1, 0, 1, . . . , N), d is the distance between two neighboring arrayelements, and θ is the zenith angle.

For a wireless communication device 1 including such an antenna array, asymbol I_(n) may be passed from a transmitter to the antenna array fortransmission by array element n. The n-th array element may thereforecreate a signal having a complex amplitude according to equation 5below:I(n)=I _(n) e ^(jϕ) ^(n) ,  Equation 5:

where I is the complex amplitude, n is the array element, j is theimaginary unit, and ϕ_(n) is an azimuthal phase shift of the signal.

In an antenna array that the azimuthal phase shift at the m-th elementϕ_(m) may be set to be equal to mϕ, wherein the spiral phase plate (SPP)may be used to introduce the desired azimuthal phase shift. By applyingthe superposition principle for the entire antenna array, the far fieldfor electric field of the antenna array can be determined according toequation 6 below:

$\begin{matrix}{{E_{\theta} = {\frac{1}{4\pi}\frac{e^{- {jkr}}}{r}{\underset{m = {{- N} + 1}}{\sum\limits^{N - 1}}{I_{m}e^{{jm}\;\phi}e^{{jkmdcos}\;\theta}}}}},} & {{Equation}\mspace{14mu} 6}\end{matrix}$

where e^(jmϕ) is an azimuthal phase term of the wavefront. Accordingly,the antenna array itself may multiplex 2N+1 independent signals, withm-th (m=−N, . . . , −1, 0, 1, . . . , N) wireless signal being imposedon the m-th OAM mode exp(jmϕ). Thus the generated OAM mode is governedby this azimuthal phase term.

The m-th transmit array antenna element may be implemented as aradiative element having an integrated SPP to introduce the azimuthalphase shift of ϕ_(m)=mϕ. Namely, to introduce the m-th OAM mode we needto azimuthally vary the thickness of the SPP according to equation 7below:h(mϕ)=mϕλ/[2π(n−1)],  Equation 7:

where n is the refractive index of material and λ is the operatingwavelength. Therefore, required azimuthally varied thickness of the SPPto introduce m-th OAM modes will be m times larger than that of OAM mode1.

However, a receive antenna array may be used to serve as an OAMdemultiplexer. The receiving OAM antenna element may introducecomplex-conjugate magnitude of e^(−jnϕ). Accordingly, the n-th antennaarray element of a receiving antenna may detect the n-th (n=−N, . . . ,−1, 0, 1, . . . , N) wireless signal corresponding to equation 8 below:

$\begin{matrix}{{E_{n} = {{\frac{1}{2\pi}{\int_{0}^{2\pi}{e^{{- {jn}}\;\phi}\frac{1}{4\pi}\frac{e^{- {jkr}}}{r}{\underset{m = {{- N} + 1}}{\sum\limits^{N - 1}}{I_{m}e^{{jm}\;\phi}e^{{jkmdcos}\;\theta}}}}}} = {\frac{1}{4\pi}\frac{e^{- {jkr}}}{r}I_{n}{e^{{jkndcos}\;\theta}.}}}}\quad} & {{Equation}\mspace{14mu} 8}\end{matrix}$

Accordingly, the received signal is proportional to the currentmagnitude for the symbol I_(n). Thus, the symbol conveyed at each OAMmode is detectable by the properly designed receive antenna array.Similar to the transmitter side, the n-th receive antenna array elementcan also be implemented as a receive antenna element integrated togetherwith a SPP, which will now introduce the azimuthal phase shift of −nϕ.This phase plate will detect only the n-th OAM and reject the other OAMmodes, effectively performing the action described by Equation 8.

As a result, the wireless communication device 1 may, therefore, beeither antenna including, e.g., a circular traveling wave antenna,spiral parabolic antenna, dual mode antenna, or other suitable antenna,or it may be an antenna array, such as, e.g., a circular antenna array,linear antenna array, planar antenna array, or conformal antenna array,or other suitable antenna array. Such antennas may be used to conveysymbols by multiplexing symbols across OAM modes generated by thewireless communication device 1.

Referring now to FIG. 2, a RF transmitter and an antenna array elementfor wireless communication with OAM-modes-enabled securemultidimensional coded modulation is illustratively depicted inaccordance with one embodiment of the present principles.

According to aspects of the present invention, wireless communicationmay be performed using transmit electronics, including e.g., atransmitter 100 which may be configured to transmit a sequence ofsymbols 10 via a transmit OAM antenna element 120 of a transmit OAMantenna array. The transmitter 100 may include an encoder 102. Theencoder 102 may be configured as, e.g., a low-density parity check(LDPC) encoder, however other types of encoders are contemplated, suchas turbo-product encoder. The encoder 102 may encode the symbol sequence10 and send the encoded sequence to a serial to parallel (S/P) converter104.

The S/P converter 104 may be configured to convert a serial stream ofsymbols from the symbol sequence 10 into multiple parallel streams. ForM symbols, the S/P converter 104 will generate log₂(M) bits. These bitscorresponding to the encoded and converted symbol sequence 10 may thenbe mapped to a 2-dimensional constellation space by a 2-D mapper 106.The mapping may be embodied as, e.g., a look-up table (LUT), but othermethods are possible, such as an algorithm based mapping or othersuitable mapping methods. Accordingly, each symbol in the sequence ofsymbols 10, upon encoding and conversion, is mapped to a 2-dimensionalsignal constellation.

The signal constellation for the original symbol sequence 10 may bemultiplexed across multiple channels. For example, the mapped sequencemay be multiplexed across two channels, such as, e.g., an in-phasechannel and a quadrature channel. Accordingly, the signal constellationcoordinates for the symbol sequence 10 are split between an in-phasechannel 10 a and quadrature channel 10 b after mapping at the mapper106. The in-phase and quadrature channels 10 a and 10 b may then undergomodulation process by a discrete-time (DT) modulator 110. The DTmodulator 110 may include modulation components to prepare the channels10 a and 10 b for transmission, including, e.g., up-samplers 112 a and112 b, pulse shapers 114 a and 114 b and a direct digital synthesizer116.

According to an embodiment of the present invention, both of thein-phase channel 10 a and the quadrature channel 10 b be prepared forphase modulation and quadrature amplitude modulation, respectively bythe modulator 110. Accordingly, each channel 10 a and 10 b may beup-sampled from the original sample rate by an in-phase up-sampler 112 aand a quadrature up-sampler 112 b respectively.

Each channel 10 a and 10 b may subsequently be pulse shaped bycorresponding filters, such as, e.g. an in-phase pulse shaper 114 a andquadrature pulse shaper 114 b, respectively. The pulse shapers 114 a and114 b may shape pulses corresponding to the up-sampled symbols byperforming a discrete-time (DT) convolution sum of the up-sampledsignals 10 a and 10 b, and an impulse response at the pulse shapers 114a and 114 b. The impulse response may be a function of the samplingperiod T of signals 10 a and 10 b. Accordingly, in-phase and quadratureDT pulses are obtained for each constellation coordinate.

The DT pulses may then be modulated by baseband functions in order tofurther improve the spectral efficiency, such as, e.g., by Slepiansequence baseband functions. The baseband functions may be applied by acomponent such as, e.g., a direct digital synthesizer 116. The directdigital synthesizer 116 may generate an in-phase DT carrier and aquadrature DT carrier. When combined using mixers 108 a and 108 b withthe in-phase DT pulses and the quadrature DT pulses, respectively, thepulses modulate the DT carriers to form in-phase signals 11 a andquadrature signals 11 b, respectively.

The in-phase and quadrature signals 11 a and 11 b may then be combinedand converted to analog-domain by a digital analog converter (DAC) 118into a quadrature multiplexed signal 12. Accordingly, each symbolsequence 10 may be up-converted as described above. Alternatively, theblock 110 may serve as discrete-time in-phase/quadrature (I/Q) modulatorfor any 2-D signal constellation. Each RF multiplexed/2-D modulatedsignal 12 may then be communicated to an antenna array, withcorresponding antenna array element represented by 120, such as thosediscussed above. The transmit OAM antenna element 120 may be a singleantenna; however, according to aspects of the present embodiment, theremay be several transmit OAM antenna elements 120, each imposing apre-determined OAM mode. The transmit OAM antenna element 120 thus mayoperate as discussed above, with an OAM mode being generated by a givenradiative antenna element 124. An azimuthal phase shifter 122 may beused to impose the OAM mode to be transmitted by the radiative antennaelement 124. As discussed above, the azimuthal phase shifter 122 mayinclude a SPP for imposing a pre-determined azimuthal phase shift. Theazimuthal phase shifter 122 may impose the OAM mode according to theazimuthal phase e^(jmϕ) to ensure a distinct OAM mode is produced at theradiative antenna element 124. As a result, the transmitter 100 andtransmit OAM antenna element 120 may generate and send an RF signalcorresponding to a particular symbol sequence 10 over a pre-determinedOAM mode.

Referring now to FIG. 3, a receiver for wireless communication withOAM-modes-enabled secure multidimensional coded modulation isillustratively depicted in accordance with one embodiment of the presentprinciples.

According to aspects of the invention, wireless communication may beperformed using a receive OAM antenna element 220 and receiveelectronics such as, e.g., a RF receiver 200 are contemplated forreceiving a signal corresponding to a pre-determined OAM mode. To permitreception of the OAM mode carrying a signal, the receive OAM antennaelement 220 may include a receive antenna element 224 together with acomplex-conjugate (c.c.) azimuthal phase shifter 222. Similar to thetransmit OAM antenna element 120 discussed above, the receive OAMantenna element 220, according to aspects of the invention, may becombined with other receive OAM antenna elements to form the OAMdemultiplexer. The receive antenna element 224 may therefore beconfigured to receive a given OAM mode according to the c.c. azimuthalphase shifter 222. The c.c. azimuthal phase shifter 222 provides theprojection along a desired OAM mode basis function. As a result, thec.c. azimuthal phase shifter 222 detects the n-th OAM mode. Similar tothe azimuthal phase shifter 122 of the transmit OAM antenna element 120described above, the c.c. azimuthal phase shifter 222 may include a SPPto implement an azimuthal phase shift.

According to aspects of the invention, once a projection of the receivedsignal 20 has been generated from the receive antenna element 224, theprojection may be demodulated by demodulator 210 corresponding to the RFreceiver 200, starting with an analog-to-digital converter (ADC) 218.The demodulator 210 may include demodulation components, such as adirect digital synthesizer 216, matched filters 214 a and 214 b andsamplers 212 a and 212 b.

The ADC 218 may receive the OAM projection and convert it into digitalform. As a result, digital signals 21 a and 21 b are generated. Thedigital signals 21 a and 21 b may be separated into an in-phase channel21 a and a quadrature channel 21 b.

Each channel 21 a and 21 b may be down-converted with by employing,e.g., a direct digital synthesizer 216. The direct digital synthesizer216 may be configured to generate cosine and sine waveforms, and thusperform down-conversion together with mixers (multipliers) 208 a and 208b. Accordingly, the direct digital synthesizer 216 together with mixers208 a and 208 b demodulates each channel 21 a and 21 b by removing theDT carrier from the received signal 21.

The resulting pulses from the demodulated in-phase and quadraturechannels 21 a and 21 b may then be down-sampled by samplers 212 a and212 b respectively, thus performing opposite operation from that ontransmitter side. The down-sampled values may therefore provideestimates of constellation points provided in the received signal 20.Accordingly, the constellation point corresponding to each sample may bedemapped using a demapper 206.

The demapper 206 may be an a posteriori probability (APP) demapper.Accordingly, the signal samples provided by the in-phase and quadraturechannels 20 a and 20 b may be analyzed with a posteriori probabilitydetector by calculating symbol log-likelihood ratios (LLRs). The LLRswill provide a most likely estimate of a transmitted symbolconstellation point by selecting the symbol corresponding to the maximumLLR. As a result, the demapper 206 may calculate the most likely symbolscorresponding to the LLRs. The LLR get passed to the nonbinary decoder.If binary decoder is used, the bit LLRs must be calculated first fromsymbol LLRs.

Upon calculating the bit LLRs, a binary LDPC decoder 202 may decode thebit stream of bit LLRs from both of the demapped in-phase channel 20 aand quadrature channel 20 b. This decoding results in a reliableestimate of the transmitted sequence.

Accordingly, a sequence of symbols carried by an OAM mode may bereceived and demodulated by the receive OAM antenna element 220 and RFreceiver 200 to determine the original sequence.

Referring now to FIG. 4, an encryption scheme for a wirelesscommunication with OAM-modes-enabled secure multidimensional codedmodulation is illustratively depicted in accordance with one embodimentof the present principles.

According to aspects of the invention, transmit electronics, such as,e.g., a transmitter 100 and an OAM encryption stage 140 including atransmit OAM antenna array 130 a may be configured to provide OAM-basedencrypted wireless communications with the help of switch 128 a. Topermit encryption in an OAM-based manner, the OAM encryption stage iscomposed of a switch 128 a and an OAM antenna array 130 a. However, theswitch 128 a may instead be a part of the transmitter 100 or it may bean independent component. Alternatively, the switch 128 a and the OAMantenna array 130 a may be replaced by an adaptive, reconfigurable, OAMantenna element.

An input sequence 10 a including user data may be encoded and modulatedby a RF transmitter 100, such as a transmitter 100 discussed above. Themodulated signal may then be communicated to the switch 128 a at thetransmit OAM antenna array 130 a. The switch 128 a may be configured torandomly select a radiative antenna element 124(0) through 124(N−1) suchthat the selected radiative antenna element yields a non-negative OAMbasis function (i.e. e^(jnϕ), n=0, 1, . . . , N−1). These radiativeantenna elements 124(0) through 124(N−1) form transmit OAM antennaelements with non-phase shifted radiative antenna element 124(0) or anazimuthal phase shifter 122(1) through 122(N−1) having a positive index(i.e., a non-negative index). As a result, an unpredictable OAM modewill be used to carry the transmitted signal.

The transmitted signal may then be received by a receive OAM antennaarray 230. The receive OAM antenna array 230 may include receive antennaelements 224(0) through 224(N−1), each of which has been followed by acomplex-conjugate (c.c.) azimuthal phase shifter 222(1) through 222(N−1)with a corresponding index to each of the radiative antenna elements124(0) through 124(N−1), thus forming receive OAM antenna elements. Forexample, as described above, the radiative antenna elements 124(0)through 124(N−1) may have non-negative indices. To reconstruct thesignal carried in the OAM mode, the c.c. azimuthal phase shifters 222(1)through 222(N−1) for the receive antenna elements 224(1) through224(N−1), respectively, may be complex conjugates to each of theradiative antenna elements 124(1) through 124(N−1), and thus havenon-positive phase shift indices. Because radiative antenna element124(0), for example, has no phase shift, receive antenna element 224(0)likewise needs no phase shift.

Because the signal is carried by only a single OAM mode, the correct OAMmode carrying the signal must be found. Since each OAM mode is generatedby a separate radiative antenna element 124(0) through 124(N−1), the OAMmode carrying the signal will have a unique complex index imposed by thecorrect radiative antenna element 124(0) through 124(N−1). As a result,only the receive antenna element 224(0) through 224(N−1) with thecorrect complex conjugate index corresponding the OAM mode carrying thesignal will produce a signal peak. The remaining elements will outputonly noise. Therefore, a maximum input selector 228 may be used todetermine which receive antenna element 224(0) through 224(N−1)generates an output with a strong signal peak. The output correspondingthe strong signal peak will be deteinined by the maximum input selector228 as the correct output.

Upon determining the correct output, the maximum input selector 228 maycommunicate the output to receive electronics, such as, e.g., a receiver200 to be demodulated by a demodulator such as the one described above.Accordingly, the receiver 200 will reconstruct the most likely sequence20 a from the transmitted OAM mode corresponding to the user data 10 a.Accordingly, the user data 10 a may be transmitted in a secure,encrypted fashion.

Alternatively, the switch and the antenna array may be replaced with anadaptive, reconfigurable, OAM antenna element, which can detect thesignal transmitted over wireless link by performing the correctcomplex-conjugate OAM mode. This approach requires the pre-sharing aninitial seed between the transmitter and the receiver. For example, thereconfigurable SPP can be tuned by changing the thickness by thermaland/or piezoelectric means.

Referring now to FIG. 5, a masking scheme for a wireless communicationwith OAM-modes-enabled secure multidimensional coded modulation isillustratively depicted in accordance with one embodiment of the presentprinciples.

According to aspects of the present invention, OAM-based securecommunication may include masking data with noisy transmissions. Forexample, a transmitter 100 may include an OAM masking stage 150 forgenerating an OAM carrier signal containing a random sequence 10 b ofinformation using a masking OAM antenna array 130 b. The random sequence10 b may be generated by, e.g., a Gaussian random generator. TheGaussian random generator may be a separate component, or it may be apart of the transmitter 100. Because the random sequence 10 b isgenerated by a Gaussian random generator, no LDPC encoder is necessaryfor the random sequence 10 b. However, other methods of generating arandom noisy sequence are contemplated.

As discussed above, a transmitter 100 may multiplex the random sequence10 b across RF domains, such as in-phase channels and quadraturechannels. However, the random sequence 10 b could also skip multiplexingacross RF domains. The transmitter 100 may then communicate the randomsequence 10 b to the masking OAM antenna array 130 b via a switch 128 b.The switch 128 b may select one or more of masking radiative antennaelements 124(1)′ through 124(N−1)′ to generate a signal in an OAM modeor a superposition of OAM modes.

To generate the OAM mode that will carry the signal, the random sequence10 b may be imposed on different OAM modes by one or more masking OAMantenna elements including one or more of azimuthal phase shifters122(1)′ through 122(N−1)′ corresponding to the selected maskingradiative antenna elements 124(1)′ through 124(N−1)′. Accordingly, therandom sequence 10 b may be applied to particular OAM modes to carry therandom noisy sequence 10 b.

By generating an OAM mode carrier for the random sequence 10 b, a signalof Gaussian randomly generated data (Gaussian noise) is transmitted withparticular OAM modes. The Gaussian noise may be transmitted concurrentlywith an actual data signal, such as described above. The actual datasignal may be encrypted or unencrypted, such as through systems andmethods described above. As a result, the Gaussian noise may mask theactual data signal by obfuscating any data structure in both time andfrequency domains.

The masking radiative antenna elements 124(1)′ through 124(N−1)′ may beconfigured to only generate signals having negative OAM indices (suchas, e.g., e^(−jnϕ)). Because OAM basis functions are orthogonal, thede-masking stage is not needed on receiver side, the data receiving OAMantenna element array will not receive the noisy signal, but only thesignal from data carrying waves from antenna elements having the correctcomplex conjugates. As a result, the noise is filtered out at thereceiver without the need for any additional equipment.

Accordingly, a data carrying OAM mode or modes may be accompanied by oneor more noise sources carrying OAM modes for masking in the time- andfrequency-domains. The data carrying OAM mode or modes may be eitherencrypted or unencrypted. A receiver may then be used to automaticallyfilter out the noise carrying OAM modes.

Referring now to FIG. 6, a transmit antenna array configuration for OAMmultiplexing and a receive antenna array for OAM demultiplexing areillustratively depicted in accordance with one embodiment of the presentprinciples.

According to aspects of the invention, a transmit OAM antenna array 130including multiple OAM antenna elements 120(N−1)′ through 120(N−1)having corresponding radiative antenna elements 124(N−1)′ through124(N−1) and azimuthal phase shifters 122(N−1)′ through 122(N−1), eachcorresponding to a transmitter 100(N−1)′ through 100(N−1), may be usedto multiplex signals across OAM modes. Each radiative antenna element ofthe radiative antenna elements 124(N−1)′ through 124(N−1) will generatea different OAM mode. Each OAM mode may also correspond to an OAM basisfunction governing its generation e^(jnϕ). The OAM modes that may begenerated may include both positive and negative OAM mode indices. As aresult, since in basis functions e^(jnϕ), the azimuthal index m=−N, . .. , −1, 0, 1, . . . , N, there are 2N+1 OAM modes. As a result, therewill likewise be 2N+1 transmit antenna radiative elements (i.e.,124(N−1), . . . , 124(1), 124(0), 124(1)′, . . . , 124(N−1)′) and 2N+1set of transmit electronics, such as, e.g., transmitters (i.e.,100(N−1), . . . , 100(1), 100(0), 100(1)′, . . . , 100(N−1)′).

A data sequence, such as data sequence 10(N−1) may be communicated totransmit electronics, such as, e.g., a RF transmitter 100, includingtransmitter 100(N−1). The transmitter 100(N−1) may be a transmitter suchas, e.g., the RF transmitter described above. The transmitter 100(N−1)may therefore, prepare the data sequence 10(N−1) for transmissionthrough the transmit OAM antenna array 130. In doing so, the transmitter100(N−1) may, for example, modulate the data sequence 10(N−1) across anin-phase channel and a quadrature channel.

Once the data sequence 10(N−1) is prepared for transmission, the datasequence is passed to the transmit OAM antenna array 130 to be azimuthalphase shifted by a transmit azimuthal phase shifter 122(N−1), such as,e.g. an SPP described above. The transmit azimuthal phase shifter122(N−1) will impose the data sequence on the corresponding OAM modefollowed by the radiative antenna element 124(N−1). The combination ofthe azimuthal phase shifter 122(N−1) and radiative antenna element124(N−1) form a transmit OAM antenna element 120(N−1). Accordingly, anOAM mode is generated by the radiative antenna element 124(N−1)according to the phase shift by the transmit azimuthal phase shifter122(N−1). This OAM mode may carry the data sequence 10(N−1). Because OAMmodes are mutually orthogonal, the 2N+1 OAM modes carrying each of thedata sequences (i.e. 10(N−1), . . . , 10(1), 10(0), 10(1)′, . . . ,10(N−1)′) may be independent from one another, and thus separatelygenerated and received. As a result, the transmitter 100 and transmitOAM antenna array 120 may multiplex 2N+1 independent data sequencesacross OAM modes.

Accordingly, the RF transmitter 100 and transmit OAM antenna array 130may have a corresponding receive OAM antenna array 230 and receiver 200.Similar to the transmitter 100 and transmit OAM antenna array 130, thereceive OAM antenna element array 230 and the receiver 200 may have 2N+1receive OAM antenna elements 220(N−1), . . . , 220(1), 220(0), 220(1)′,. . . , and 220(N−1)′ and 2N+1 receive electronics, such as, e.g., RFreceivers 200(N−1), . . . , 200(1), 200(0), 200(1)′, . . . , and200(N−1)′, respectively. Each receive OAM antenna elements 220(N−1), . .. , 220(1), 220(0), 220(1)′, . . . , and 220(N−1)′ includescorresponding receive antenna elements 224(N−1), . . . , 224(1), 224(0),224(1)′, . . . , and 224(N−1)′ followed by corresponding c.c. azimuthalphase shifters 222(N−1), . . . , 222(1), 222(1)′, . . . , and 222(N−1)′according to an OAM basis function index that is a complex conjugate tothe index of each corresponding radiative antenna element 124(N−1), . .. , 124(1), 124(0), 124(1)′, . . . , and 124(N−1)′. As a result, eachreceive antenna element 224(N−1), . . . , 224(1), 224(0), 224(1)′, . . ., and 224(N−1)′ may detect an independent and orthogonal OAM mode. Thecombination of each receive antenna element 224(N−1), . . . , 224(1),224(0), 224(1)′, . . . , and 224(N−1)′ with corresponding c.c. azimuthalphase shifter 222(N−1), . . . , 222(1), 222(1)′, . . . , and 222(N−1)′forms a receive OAM antenna element of the receive OAM antenna array230.

For example, when radiative antenna element 124(N−1) generates andtransmits an OAM mode having the index e^(j(N−1)ϕ) and carrying datasequence 10(N−1), a receive antenna element 224(N−1) may be configuredto detect that OAM mode using the complex conjugate index ofe^(−j(N−1)ϕ). Each receive antenna element 224(N−1), . . . , 224(1),224(0), 224(1)′, . . . , and 224(N−1)′ may similarly be configured toreceive the OAM mode carrying each respective data sequence 10(N−1), . .. , 10(1), 10(0), 10(1)′, . . . , 10(N−1)′. As a result, data sequencesfrom a different user gets demultiplexed from across OAM modes, thusreproducing the original transmitted data.

Referring now to FIG. 7, a 2 L-dimensional modulator for wirelesscommunication with OAM-modes-enabled secure multidimensional codedmodulation is illustratively depicted in accordance with one embodimentof the present principles.

According to aspects of the present invention, the DOF employed formultidimensional multiplexing including OAM modes may includemultiplexing across basis functions in a Multiple Input Multiple Output(MIMO) implementation. This implementation, according to aspects of thepresent invention, includes utilizing baseband basis functions to mapdata sequences 10(1), . . . , 10(2L) to a signal constellation ratherthan mapping in-phase and quadrature sequences, such as described above.Accordingly, transmit electronics, such as, e.g., a transmitterincluding a modulator 110 is contemplated.

The modulator 110 imposes the data sequences 10(1), . . . , 10(2L) on 2LSlepian sequences, serving as impulse responses of correspondingfilters. Slepian sequences have the beneficial properties of beingmutually orthogonal with a double orthogonality property, for example,Equation 9 below:Σ_(m=0) ^(L−1) s _(m) ^((l))(L _(g) ,W)s _(m) ^((k))(L _(g) ,W)=μ_(d)(L_(g) ,W)Σ_(m=−∞) ^(∞) s _(m) ^((l))(L _(g) ,W)s _(m) ^((k))(L _(g),W)=μ_(d)(L _(g) ,W)δ_(lk),  Equation 9:

where L_(g) is the sequence length, W is the discrete bandwidth, δ_(dk)is the delta function, and μ_(d) represents the ordered eigenvalues.

Due to the double orthogonality property, the baseband basis functionsthat form the projections for the baseband domain sequences 10(1), . . ., 10(2L) will stay orthogonal even outside of a desired symboltime-interval. This property serves to reduce sensitivity to intersymbolinterference (ISI) and multipath fading. When used for baseband basisfunctions, the Slepian sequences may simply be software definedfunctions.

Additionally, the baseband basis functions may be complex basisfunctions derived from the Slepian sequences. Thus, each Slepiansequence of even order can be used to create a real component of acorresponding complex basis function, and each Slepian sequence of oddorder can be used to create an imaginary component of a correspondingcomplex basis function. As described above, the real and imaginarycomponents of the corresponding complex basis functions conform to thedouble orthogonality property. As a result, for L complex basisfunctions, there will be 2L basis functions corresponding to 2L Slepiansequences. The modulator 110 may impose the data sequences 10(1), . . ., 10(2L), on baseband impulse responses of corresponding filters derivedfrom 2L Slepian sequences. As a result, the data sequences 10(2), 10(4),. . . , 10(2L) are imposed on impulse responses derived from even orderSlepian sequences and form an in-phase channel, while on the other handthe data sequences 10(1), 10(3), . . . , 10(2L−1) are imposed on theimpulse responses (e.g., filters) derived from odd order Slepiansequences and form the quadrature channel.

While described above is the use of Slepian sequences for basebandfunctions, the modulator 110 of the present invention may use of Slepiansequences to generate passband filters with passband impulse responsesderived from Slepian sequences and implemented by adjusting the gainsand phase shifts of corresponding antenna array elements. When used inthis way, 2K Slepian sequences may be used to derive 2K passband basisfunctions to form an Orthogonal Division Multiplexing DOF. Alternative,a combination of passband and baseband functions may be employed toincrease the DOF to 2LK DOF.

Upon deriving the baseband domain sequences from Slepian sequences, theyare used as impulse responses of filters, such as, e.g., pulse shapers114(1), . . . , 114(2L). The data sequences 10(1), . . . , 10(2L) areused as inputs into the up-samplers 112. The up-sampled sequences 10(1),. . . , 10(2L) are then passed to the DT pulse shapers 114, whoseimpulse responses are derived from Slepian sequences.

The outputs of DT pulse shapers of even order are combined at adder 117a to form the in-phase channel. Similarly, the outputs DT pulse shaperswith odd order are combined at adder 117 b form a quadrature channel.The resulting in-phase channel and quadrature channels are used asinputs of the direct digital synthesizer 116. The direct digitalsynthesizer 116 generates cosine and sine waveforms that areup-converted to the desired carrier frequency with the help of mixers(multipliers) 108 a and 108 b.

The in-phase and quadrature signals 11 a and 11 b may then be combinedat adder 117 c and converted to analog domain by a digital analogconverter (DAC) 118 to create a RF passband signal 12. Accordingly, theresulting RF signal 12 is a 2L-dimensional signal. The RF modulatedsignal 12 may then be forwarded to an OAM antenna element or OAM antennaelement array, as discussed above. It is also possible to use anothercontinuous-time up-converter to move the carrier frequency to mm-wave orTHz range. The OAM antenna element or OAM antenna element array mayinclude one or more OAM antenna elements, with each OAM antenna elementincluding an azimuthal phase shifter as described above, such as, e.g.SPP.

Referring now to FIG. 8, a 2L-dimensional demodulator for wirelesscommunication with OAM-modes-enabled secure multidimensional codedmodulation is illustratively depicted in accordance with one embodimentof the present principles.

According to aspects of the present invention, the OAM multiplexedsignal is processed by receive electronics, such as, e.g., an OAMdemultiplexer 210. The n-th branch provides the projection along then-the OAM mode, and this signal is passed to ADC input 22.

An ADC 218 may receive the 2L-dimensional RF signal 22 and convert itinto digital form. As a result, digital signals 21 a and 21 b aregenerated, and passed to corresponding in-phase and quadraturedown-converters (multipliers).

Each digital input 21 a and 21 b may be demodulated with a directdigital synthesizer 216. The direct digital synthesizer 216 generatesthe cosine and sine waveforms, used as DT local oscillators outputs toperform the down-conversion process at mixers 208 a and 208 b used asthe quadrature down-converters (multipliers). Accordingly, the directdigital synthesizer 216 and down-converters 208 a and 208 b perform theconversion in baseband. As a result, the received 2L-dimensional RFsignal 22 is down-converted into 2L-dimensonal baseband signals.

The baseband in-phase and quadrature signals are passed to matchedfilters 214(1), . . . , 214(2L). The matched filters 214(1), . . . ,214(2L) may be configured to include impulse responses that match the DTpulse shaping filters 114(1), . . . , 114(2L) of a 2L-dimensionalmodulator such as the modulator 110 described above. As a result, thematched filters 214(1), . . . , 214(2L) provide the projections alongthe baseband basis functions.

The resulting baseband domain pulses from the demodulated in-phase andquadrature channels 21 a and 21 b, at the outputs of matched filters212(1), . . . , 212(2L), represent projections along baseband basisfunctions down-sampled by down-samplers 212(1), . . . , 212(2L). Thedown-sampled values may therefore represent the samples of receivedconstellation points provided in the received signal 22, the estimatedconstellation coordinates 20(2), 20(4), . . . , 20(2L) are furtherpassed to the multidimensional demapper.

Each sequence may then be demapped by a demapper. The demapper may be ana posteriori probability (APP) demapper. Accordingly, the basebanddomain sequence samples 20(1), . . . , 20(2L), representing theprojections along the baseband basis functions, may be analyzed with2L-dimensional aposteriori probability demapper by calculating symbollog-likelihood ratios (LLRs). The LLRs will provide the reliabilities ofcorresponding symbols. As a result, the demapper may calculate symbolLLRs passed to nonbinary LDPC decoder. When binary LDPC codes are used,the bit LLRs need to be calculated first from symbol LLRs. The LDPCdecoder then performs iterative decoding, and generates the decodedsequence.

Referring now to FIG. 9, a coded 2L-dimensional modulator for wirelesscommunication with OAM-modes-enabled secure multidimensional codedmodulation is illustratively depicted in accordance with one embodimentof the present principles.

According to aspects of the present invention, a 2L-dimensionaltransmitter may include a multidimensional modulator, such as, e.g. a2L-dimensional modulator described above, as well as additional signalprocessing and decoding components. The additional signal processingcomponents assist to convert m independent data streams 30(1)-30(m) to a2L-dimensional multiplexed signal 32 to be sent to an antenna array fortransmission.

The independent data streams 30(1)-30(m) may be encoded by respectiveLDPC encoders 302(1)-302(m) into m independent encoded streams withcorresponding codewords. The LDPC encoders 302(1)-302(m) may employ asoftware-defined LDPC coded modulation scheme for adaptive encoding.Using such a scheme, code rates may be adapted based on time-varyingmultipath channel conditions. Thus, the independent data streams30(1)-30(m) may be encoded in way that is resistant to noise and spatialinterference.

The independent encoded streams are then written into an interleaver304. The interleaver 304 is configured to combine the independentencoded streams 30(1)-30(m) into a single data sequence for modulation.

The single data sequence at the output of interleaver 304 can then bemapped onto a signal constellation with a multidimensional mapper 306.Similar to above, the mapper 306 may be in the form of a LUT, however itmay also be algorithmically deteimined. The LUT may map the data in thesingle data sequence to a constellation space that has a dimensionalitycorresponding to a modulator that will modulate the signal. According toaspects of the present invention, the constellation space may thereforebe, similar to above, a 2L-dimensional space corresponding to 2Lbaseband functions.

The mapped data sequence may be then by modulated according to 2Lbaseband function by a 2L-dimensional modulator 310. The basebandfunctions, representing the impulse responses of a set of filters, suchas e.g., pulse shapers in 2L-dimensional modulator, as described above,may be L complex baseband functions derived from Slepian sequences toproduce a real set of L baseband functions corresponding to an in-phasechannel, and an imaginary set of L baseband functions corresponding to aquadrature channel. However, other modulation methods are contemplated.Similar to what is described in the 2L-dimensional modulator describedabove, the 2L-dimensional modulator 310 may be based on direct digitalsynthesizer to combine the in-phase and quadrature channels and performup-conversion.

The RF carrier, prior to being transmitted by an antenna array, may thenbe further up-converted by an RF up-converter to mm-wave or THz domain.The RF-upconverter may also perform frequency division multiplexing.Alternatively, the coded 2L-dimensional RF signal can be furthermultiplexed in passband orthogonal division multiplexer 318, composed of2K passband filters implemented by properly adjusting the gains andphases of elements of an antenna array, such as an OAM antenna array.According to aspects of the present invention, the passband filters'impulse responses are derived from Slepian sequences as well. The RForthogonal division multiplexing results in an RF multiplexed sequence32 across, e.g., a 4LK multidimensional signal, such as an OAM-modecarrier signal corresponding to the 2L baseband basis functions and 2Kpassband basis functions. The RF multiplexed signal 32 may be directedtowards single or multiple wireless receivers. Alternatively, the RFmultiplexed signal 32 may be used as an input to transmit OAM antenna.

Referring now to FIG. 10, a 2L-dimensional iterative demapper forwireless communication with OAM-modes-enabled secure multidimensionalcoded modulation is illustratively depicted in accordance with oneembodiment of the present principles.

According to aspects of the present invention, a receiver may include a2KL-dimensional demodulator, such as, e.g., a demodulator as describedabove, as well as additional signal processing and decoding components.The additional signal processing components assist demultiplexing of anRF multiplexed sequence 42 carrying, e.g. a 4LK-dimensional RFmultiplexed sequence, such as discussed above, to projections alongcorresponding basis functions.

Having received an OAM mode carrier by an OAM antenna array, such as onediscussed above, the carrier may be converted by the antenna array intoprojections along OAM basis functions to determine the transmitted RFmultiplexed sequence 42, thus demultiplexing the OAM mode carrier. Abandpass filter 418 may then demultiplex the RF multiplexed sequence 42.The bandpass filter 418 may perform this demultiplexing by using inversepassband basis functions corresponding to, e.g., the 2K passband basisfunctions derived from complex Slepian sequences. Alternatively, thebandpass filter 418 may be configured to select a frequency bandcorresponding to the frequency bands when signals were RF multiplexedwith FDM. As a result, the RF multiplexed sequence 42 may bedemultiplexed across frequency bands by the bandpass filter 418.

The demultiplexing the 2K passband basis functions results in a2L-dimensional sequence that is then demodulated by a multidimensionaldemodulator 410, including, e.g., a 2L-dimensional RF demodulator suchas one described above. The multidimensional demodulator 410 isconfigured to determine projections along baseband DT basis functions,for example, e.g. along baseband functions derived from Slepiansequences as described above.

A multidimensional demapper 406 a may then demap the projections basedon APP, e.g., similar to the demapping described above. The demapper 406a may operate in a 2L-dimension signal space corresponding to atransmitter with a 2L-dimension modulator, such as one described above.Accordingly, the demapper 406 a may demap the projections into symbolLLRs. The symbol LLRs will provide a most likely estimate of atransmitted symbol constellation points. When nonbinary LDPC coding isused the multidimensional demapper 406 a will provide symbol LLRs tononbinary LDPC decoder. On the other hand, when binary LDPC coding isused, the multidimensional demapper will provide symbol LLRs to bit LLRcalculator 406 b.

As a result, a bit LLR calculator 406 b uses the symbol LLRs tocalculate the most likely bits corresponding to the determined symbolconstellation points, for uncoded signals. For coded signals, the bitLLRs are calculated with the help of bit LLR calculator 406 b. The bitLLRs, representing the soft bit reliabilities, are then passed to theLDPC decoders 402. The decoded bit LLRs determine estimated originaldata sequences 40(1)-40(m) corresponding to the originally multiplexedindependent data streams.

The demapper 406 a may be subject to a bit error rate (BER) due toerrors in the signal from transmission and/or processing. As a result,it is advantageous to reduce the BER. According to aspects of theinvention, extrinsic information 44 from the LDPC decoders 402 may bepassed back to the demapper 406 a to iterate on the extrinsicinformation 44. This iteratively derived extrinsic information 44 may beemployed by the demapper 406 a to reduce the BER of demapping, thusimproving the APP calculation and determination of symbol LLRs. As aresult, better estimated original data streams 40(1)-40(m) may bedetermined.

Referring now to FIG. 11, an unconditional physical layer securityscheme for optical wireless communication with OAM-modes-enabled securemultidimensional coded modulation is illustratively depicted inaccordance with one embodiment of the present principles.

According to aspects of the present invention, physical-layer securitymay be enhanced by employing multiplexing across OAM modes. The OAMmodes may be used to increase the dimensionality of the signal and thesignal constellation space, thus increasing secrecy capacity and securekey rates. Accordingly, a signal may be transmitted from a transmitter500 to an intended receiver 600 in an unconditionally securetransmission, such that the signal is secure from any interceptingreceiver 700.

The transmitter 500 may include multidimensional modulation scheme 506.The multidimensional modulation scheme 506 may include, e.g., anarbitrary waveform generator, one or more multidimensional modulatorscombined with one or more a multidimensional multiplexer, or anysuitable scheme for performing subcarrier multiplexing. Themultidimensional modulation scheme 506 may be employed to performsubcarrier multiplexing (SCM) of a signal including multiple independentdata streams. Thus, the multidimensional modulation scheme 506 mayinclude, e.g., an arbitrary waveform generator, one or moremultidimensional modulators (such as an RF modulator or other modulator)combined with one or more multidimensional multiplexers, or any suitablescheme for performing subcarrier multiplexing. The data streams mayinclude, e.g., data, a cryptographic key, or both.

According to aspects of the present invention, the multidimensionalmodulation scheme 506 may be a modulator such as, e.g., an RF modulatoras described above for generating an in-phase channel and quadraturechannel for the independent data streams. The SCM may therefore includephase-shift keying (PSK) to RF modulate a subcarrier in an in-phasechannel, or the SCM may include quadrature amplitude modulation (QAM) toRF modulate the subcarrier across both in-phase and quadrature channels.As described above, each of the subcarrier channels may additionallyinclude multidimensional modulation by employing Slepian-sequencederived baseband basis functions. Thus, as described above, thedimensionality of the signal space may be increased to a determinedamount.

The transmitter 500 may include an optical I/Q modulator 510 to furthermodulate the multidimensional in-phase and quadrature channels generatedby the multidimensional modulation scheme 506, and convert them tooptical domain. To accomplish this, an optical source 502, such as,e.g., a transmit laser diode or an ASE noise source, may provide anoptical signal to the optical I/Q modulator 510. The optical I/Qmodulator 510 may therefore further modulate the modulated subcarrierfrom the multidimensional modulation scheme 506 into the optical signalfrom the optical source 502 to generate an optically modulatedmultidimensional signal/supercarrier.

The optically modulated multidimensional signal/supercarrier may be usedas an input to an optical OAM multiplexer 524. The optical OAMmultiplexer 524 may include an azimuthal phase shifter, such as, e.g.,an SPP, computer generated hologram, or grating. This optical OAMmultiplexer 524 may be included with the optical I/Q modulator 510, andmay be similar to OAM multiplexers including a SPP as described above,except designed for optical frequencies. Thus, the optically modulatedmultidimensional signal/supercarrier may be imposed on an OAM mode toform an OAM carrier.

In addition to OAM multiplexing, the polarization division multiplexing(PDM) can also be used. The polarization controller 504 is used toensure that photons are properly polarized.

A variable optical attenuator 508 is then used to reduce the signallevel down to the shot noise level.

As a result, the transmitter 500 generates a signal constellation spacethat combines optical and wireless features to generate a highlymultidimensional signal. This highly multidimensional constellationspace ensures that an intercepting receiver 700 that intercepts a givenDOF will only receive a single constellation point amongst the manyindependent data streams multiplexed in the constellation. As a result,the intercepting receiver 700 will be unable to receive a large portionof the signal, and therefore will be unable to reproduce the transmitteddata. In the case that a raw key is sent in the signal, the interceptingreceiver 700 will be unable to fully intercept the raw key transmission,and thus be unable to compromise the security of a message. Moreover,even if OAM modes are coupled, security will still not be compromisedbecause multiple DOF are implemented.

The quantum channel 800 may be any communication medium suitable forcarrying quantum information, such as orbital angular momentum,including, e.g., optical fiber, and optical wireless communication link.

Additionally, an intended receiver 600 is configured to receive thesecure transmission and extract the data from the supercarrier. Theintended receiver 600 may use classical coherent optical detection withphase noise cancellation (PNC) to control excess noise and thus receivea message or shared key from the transmitter 500 with low bit-errorrate.

For example, the intended receiver 600 includes an optical OAMdemultiplexer 624. The optical OAM multiplexer 624 may include acomplex-conjugate (c.c.) azimuthal phase shifter, such as, e.g., a SPP,computer generated hologram, or grating. This optical OAM demultiplexer624 may be similar to OAM demultiplexers including a SPP as describedabove, except designed for optical frequencies. Thus, the optical OAMdemultiplexer extracts projections from the transmitted OAM carrier.

The receiver 600 will additionally include a balanced coherent detector608. The projections may be passed through a polarization controller 604a similar to the polarization controller 504 discussed above. Thepolarization controllers 604 and 604 a are used to ensure thatpolarization states of received signal and local oscillator signal arematched. Alternatively, the polarization beam splitters may be employedto participate in polarization division demultiplexing.

The balanced coherent optical detector 608 is configured to receive theprojections and extract the PSK, QAM, or multidimensional basebandsignals from the supercarrier, for example, e.g., similar todemodulators described above. Balanced detector 608 mixes the receivedoptical signal and local laser signals to provide the correspondingprojections along in-phase and quadrature basis functions.

A subcarrier demultiplexer 610 may include components for demultiplexingthe subcarrier RF channels on different RF subcarrier frequencies, togenerate multiple multidimensional signals passed to PNC devices.

There may be as many PNC devices as there are independent data streamsinput into the transmitter 500. The PNC devices 602 a, 602 b and 602 care configured to cancel the effects of laser phase noise and any randomphase shift introduced by the quantum channel 800. According to aspectsof the present invention, each PNC device 602 a, 602 b and 603 cincludes two square operators, one addition operator, a digital DCcancellation block and a low pass filtering block. Squaring in-phase andquadrature channels of the optical carrier cancels the effects of laserphase noise and any random phase shifts introduced by the quantumchannel, thus reducing bit-rate error. Accordingly, the originalindependent data streams may be estimated with low bit-rate error in ahighly secure fashion. After PNC each multidimensional signal furtherundergoes the multidimensional demodulation process described above.

After that, the reverse information reconciliation and privacyamplification are further used to remove any correlation with respect toan eavesdropping receiver 700.

The secure key rates (SKRs) may also be very high because SKR isproportional to the number of DOF. Thus, the proposed RF-subcarrierassisted CV-QKD can be orders of magnitude greater than other quantumkey distribution schemes.

Another approach to enable unconditional security over RF links is byemploying the microwave illumination approach, in which we can entanglemm-wave/THz/RF wave and optical beam, so that through flood-light(FL)-QKD approach we can achieve multi-Gb/s secure key rates overmm-wave/THz/RF links. In this scenario, the weak optical beam is used tomonitor Eve's intrusion, while mm-wave/THz/RF link is used for raw-keytransmission.

Referring now to FIG. 12, a system/method for wireless transmission withOAM-modes-enabled secure multidimensional coded modulation isillustratively depicted in terms of flow-chart in accordance with oneembodiment of the present principles.

According to aspects of the present invention, several sequences ofsymbols may be multiplexed together using OAM modes for securemultidimensional coded modulation. According to aspects of the presentinvention, each of the symbol sequences will be encoded and mapped to acorresponding constellation space using constellation coordinates atblock 801. The encoding may include, e.g., performing LDPC encoding foreach symbol sequence, and mapping may be performed with, e.g., alook-up-table.

At block 802, the constellation coordinates will be multiplexed acrossan in-phase channel and a quadrature channel. The multiplexing mayinclude mapping to each of the in-phase channel and the quadraturechannel using quadrature amplitude multiplexing. Alternatively, thephase-shift keying (PSK) employing only in-phase channel maybe used orquadrature amplitude modulation (QAM) by employing both in-phase andquadrature channels. The multiplexing may further include up-samplingeach channel based on the sampling period and symbol duration, and pulseshaping each channel using an appropriate impulse response.

At block 803, RF modulation will be performed on each channel togenerate an RF modulated signal. RF modulation may include imposing RFcarriers on each channel using, e.g., a direct digital synthesizer andmixers. Once each channel is carried by a respective RF carrier, thechannels may be recombined and converted to analog domain with, e.g., adigital to analog converter.

At block 804, an antenna element of an OAM antenna element array may beazimuthal phase shifted to generate a particular orbital angularmomentum (OAM) mode. Azimuthal phase shifting of the OAM antenna elementmay include imposing the signal on OAM basis function (e^(jmϕ)).

At block 805, the RF modulated signal will be imposed on the OAM mode bypassing the modulated signal from azimuthal phase shifter to theradiative antenna element. Encryption may be performed by, e.g.,including multiple OAM modes corresponding to multiple OAM antennaelement, where the RF modulated signal is imposed on a random one of themultiple OAM modes.

At block 806, each symbol sequence may be imposed on an orthogonal OAMmode carrier by transmitting each symbol sequence from a correspondingOAM antenna element of the OAM antenna element array. Accordingly, eachOAM antenna element will introduce a distinct azimuthal phase shiftaccording to the desired OAM mode. As a result, the transmitted signalfrom each OAM antenna element will be carried by an OAM mode that isorthogonal to any other OAM mode, and thus is independent from any otherOAM mode carrier. Multiple signals will be imposed on different OAMmodes and combined together. Masking may be performed for thetransmitted orthogonal OAM mode carriers by including noisy OAM modecarriers for OAM modes having a negative index in the azimuthal phaseterm, to hide any data structure in both time- and frequency-domains foran unauthorized user.

Referring now to FIG. 13, a system/method for receiving a wirelesstransmission with OAM-modes-enabled secure multidimensional codedmodulation is illustratively depicted in flow-chart fashion inaccordance with one embodiment of the present principles.

According to aspects of the present invention, a set of OAM mode carriersignals may be received by an OAM antenna element array, and symbolsequences corresponding to the OAM mode carrier signals may be estimatedtherefrom. For each of the transmitted OAM mode carriers, a respectiveOAM antenna element of the OAM antenna element array will receive theOAM mode carrier signal by having a complex-conjugate azimuthal phaseshift that corresponding to the received OAM mode carrier at block 901.Thus, the receive antenna element may have an azimuthal phase shift withan index that is a complex conjugate to the azimuthal phase shift termgoverning the far field transmission of the OAM mode carrier signal. Toperform decryption on an OAM carrier signal that has been encrypted asdescribed above, multiple OAM antenna elements may be employed toreceive signals where only one of the multiple OAM antenna elements hasthe correct complex conjugate azimuthal phase term. A selection devicemay therefore be employed to select the signal from the OAM antennaelement having the largest current amplitude corresponding to a receivedsignal. Alternatively, an adaptive, reconfigurable, SPP can be used toget the desired projection.

At block 902, projections are then extracted from the OAM mode carriersignal corresponding to an RF modulated signal. These projections are infact the discrete-time projections along basis function that correspondto the RF modulated signal.

At block 903, RF demodulation is performed on the projections toestimate constellation coordinates. RF demodulation may be performed bya demodulator including, e.g., a directed digital synthesizer, combinedwith mixers, to extract in-phase and quadrature channels from theprojections, matched filters that are configured to provide theprojections along the baseband basis functions, derived from Slepiansequences.

At block 904, a posteriori probability is calculated to determine symbollog-likelihood ratios corresponding to each candidate symbol. The symbolLLRs have been calculated in APP demapper.

At block 905, the symbol log-likelihood ratios are converted to bitlog-likelihood ratios.

At block 906, the decoding is performed by, e.g., LDPC decoders.Accordingly, a set of OAM mode carriers may be received by an OAMantenna element array and the carried symbol sequence for each OAM modecarrier may be estimated at a receiver to obtain the original sequences.

Referring now to FIG. 14, a system/method for wireless transmission withmultidimensional coded modulation using baseband functions isillustratively depicted in accordance with one embodiment of the presentprinciples.

According to aspects of the present invention, a set of symbols may bemultiplexed using OAM modes for secure multidimensional codedmodulation. The set of symbols may include a number of symbol sequences.According to aspects of the present invention, each of the symbolsequences will be encoded and mapped to a corresponding constellationdiagram using constellation coordinates at block 1001. The encoding mayinclude, e.g., performing LDPC encoding for each symbol sequence, andmapping may be performed with, e.g., a look-up-table.

At block 1002, the constellation coordinates will be multiplexed acrossmultiple mutually orthogonal baseband basis functions. Thisimplementation, according to aspects of the present invention, includesutilizing baseband basis functions derived from Slepian sequences to mapbaseband domain sequences to a signal constellation rather than mappingto in-phase and quadrature coordinates, such as described above.

At block 1003, the baseband domain sequences are split into an in-phasechannel corresponding to even order Slepian sequence components, and aquadrature channel corresponding to odd order Slepian sequencecomponents. Because Slepian sequences are real, 2L Slepian sequences areused to create L complex basis functions. The baseband domain sequencesderived from the Slepian sequences are used as impulse responses ofcorresponding filters, including pulse shapers in 2L-dimensionalmodulator described above.

While described above is the use of Slepian sequences for basebandfunctions, the present invention also contemplates the use of Slepiansequences to generate passband filters by deriving impulse responses byproperly adjusting the gains and phase shifts of antenna array elements.When used in this way, 2K passband basis functions are used to enablethe Orthogonal Division Multiplexing DOF.

At block 1004, RF modulation will be performed on each channel togenerate an RF modulated signal. RF modulation may include imposing RFcarriers on each channel using, e.g., a direct digital synthesizer andmixers. Once each channel is carried by a respective RF carrier, thechannels may be combined and converted to analog domain with, e.g., adigital to analog converter.

At block 1005, an OAM antenna element is used to impose the azimuthalbasis function (e^(jmϕ)) and transmit such a signal towards the remotedestination.

At block 1006, the RF modulated signal will be imposed on the OAM modeof the OAM antenna element by transmitting the RF modulated signal froman azimuthal phase shifted radiative element. Encryption may beperformed by, e.g., including multiple OAM modes corresponding tomultiple OAM antenna elements, where the RF modulated signal is imposedon a random one out of the multiple OAM modes available. Randomlyimposing the RF modulated signal on the one of the multiple OAM modesmay be performed using a random switch between the RF modulator and themultiple OAM antenna elements.

At block 1007, each symbol sequence may be imposed on an orthogonal OAMmode carrier by transmitting each symbol sequence from a correspondingOAM antenna element of the OAM antenna element array. Accordingly, eachOAM antenna element may have a distinct azimuthal phase shift of itsazimuthal phase term to form a distinct OAM mode with each OAM antennaelement. As a result, the transmitted signal from each OAM antennaelement will be carried by an OAM mode that is orthogonal to any otherOAM mode, and thus it is independent from other OAM mode carriers.Masking may be performed for the transmitted orthogonal OAM modecarriers by including noisy OAM mode carriers for OAM modes having anegative index in the azimuthal phase term to hide the data structure toan unauthorized user.

Referring now to FIG. 15, a system/method for receiving a wirelesstransmission with multidimensional coded modulation using basebandfunctions is illustratively depicted with help of flow-chart inaccordance with one embodiment of the present principles.

According to aspects of the present invention, a set of OAM mode carriersignals may be received by an OAM antenna element array, and symbolsequences corresponding to the OAM mode carrier signals may be estimatedtherefrom. For each of the transmitted OAM mode carriers, a respectivereceive antenna element of the OAM antenna element array will receivethe OAM mode carrier signal by having an azimuthal phase shift thatcorresponds to the received OAM mode carrier at block 1101. Thus, thereceive antenna element may have an azimuthal phase shift with an indexthat is a complex conjugate to the azimuthal phase shift term governingthe far field transmission of the OAM mode carrier signal. To performdecryption on an OAM carrier signal that has been encrypted as describedabove, multiple OAM antenna elements may be employed to receive signalswhere only one of the multiple OAM antenna elements has the correctazimuthal phase term. A selection device may therefore be employed toselect the signal from the OAM antenna element having the largestcurrent amplitude corresponding to a received signal. Alternatively, theadaptive, reconfigurable, SPP maybe be used to detect the desired OAMmode.

At block 1102, projections are then extracted from the OAM modes carriersignal with each projection corresponding to a 2L-dimensional RFmodulated signal.

At block 1103, RF demodulation is performed on the projections todetermine in-phase and quadrature channels, down-convert the in-phasechannel to baseband domain sequences corresponding to even order Slepiansequences, and down-convert the quadrature channel to baseband domainsequences corresponding to odd order Slepian sequences. RF demodulationmay be performed by a demodulator including, e.g., a directed digitalsynthesizer and mixers to extract in-phase and quadrature channels fromthe projections.

At block 1104, re-sample each baseband sequence after passing throughmatched filters and down-sample each match filter output correspondingto each baseband domain sequence. The matched filters may be configuredto have impulse responses that match the DT pulse shaping filters of a2L-dimensional modulator such as the modulator described above. As aresult, the matched filters determine pulses corresponding to each ofthe signals that match baseband domain basis functions, to outputbaseband domain pulses.

The resulting baseband domain pulses from the demodulated in-phase andquadrature channels may then be down-sampled by corresponding samplers,after proper match filtering, respectively. The down-sampled signals maytherefore represent estimates of constellation points provided in thereceived signal.

At block 1105, symbol sequences corresponding to original symbolsequences carried in each of the transmitted OAM mode carriers areestimated. Estimating the symbol sequences may include, e.g.,calculating a posteriori probability to determine symbol log-likelihoodratios corresponding to each candidate symbol, converting the symbollog-likelihood ratios to bit log-likelihood ratios, and decoding the bitlog-likelihood ratios to obtain estimates of the original sequences.

Referring now to FIG. 16, unconditional physical layer security schemefor optical wireless communication with OAM-modes-enabled securemultidimensional coded modulation is illustratively depicted inaccordance with one embodiment of the present principles.

According to aspects of the present invention, unconditionalphysical-layer security may be enhanced by employing modulation acrossOAM modes. The OAM modes may be used to increase the dimensionality ofthe signal and the signal constellation space, thus increasing secrecycapacity and secure key rates. Accordingly, a signal may be transmittedfrom a transmitter to an intended receiver in an unconditionally securetransmission, such that the signal is secure from any interceptingreceiver.

At block 1201, the transmitter generates an arbitrary waveform with amultidimensional modulation scheme to perform subcarrier multiplexing(SCM) of a signal including multiple independent data streams. The datastreams may include, e.g., data, a cryptographic key, or both.Accordingly, the multidimensional modulation scheme may be e.g., anarbitrary waveform generator, or a RF multidimensional modulator suchas, e.g., a modulator as described above. The SCM may employ phase-shiftkeying (PSK) or quadrature amplitude modulation (QAM) constellationpoints. As described above, each of the channels may include multiple amultidimensional modulation by employing Slepian-sequence derivedbaseband basis functions.

At block 1202, the transmit laser generates an optical beam.

At block 1203, the transmitter sends the in-phase and quadraturechannels generated by the multidimensional modulation scheme to anoptical modulator. The optical modulator may be an I/Q opticalmodulator. Further, several multidimensional optical signals maybecombined by using OAM optical multiplexer and polarization divisionmultiplexing devices.

As a result, the transmitter generates a signal constellation space thatis highly multidimensional. This highly multidimensional constellationspace ensures that an intercepting receiver that intercepts a given DOFwill only receive a single constellation point amongst the manyindependent data streams multiplexed in the constellation. As a result,the intercepting receiver will be unable to reconstruct the transmittedsignal. In the case that a raw key is sent in the signal, theintercepting receiver will be unable to intercept the full key, and thusbe unable to compromise the security of a message. Moreover, even if OAMmodes are coupled, security will still not be compromised becausemultiple other DOF are implemented, such as PSK and QAM. Therefore,risks of compromise due to OAM mode coupling are reduced.

At block 1204, the transmitter may also attenuate the supercarrier usinga variable optical attenuator and transmit the supercarrier across thequantum channel. The supercarrier containing the data to be transmittedwill be passed through the variable optical attenuator to reduce thepower of the signal for optical transmission through a quantum channel.The quantum channel may be any communication medium suitable forcarrying quantum information, such as orbital angular momentum,including, e.g., optical fiber and optical wireless communication link.

At block 1205, an intended receiver receives the secure transmissionwith a balanced coherent detector to extract the PSK and QAM carriers.The supercarrier may be passed through a polarization controller toensure that its polarization is matched to the local laser polarization.The balanced coherent detector is configured to receive the supercarrierand extract the PSK and/or QAM carriers from the supercarrier, forexample, e.g., by properly mixing the received optical signal and locallaser signal, followed by photodetection process, to obtain theprojections along in-phase and quadrature channels.

At block 1206, a subcarrier demultiplexer demultiplexes the PSK and QAMcarriers corresponding to the in-phase channel and the quadraturechannel to generate estimates of constellation signals. The subcarrierdemultiplexer may include components for demultiplexing the in-phase andquadrature channels, such as, e.g. components as described in receiversabove including an APP demapper and LLR calculator. Accordingly, thesubcarrier demultiplex demultiplexes the PSK and QAM subcarriers togenerate estimated constellation points.

At block 1207, the estimated constellation signals undergo phase noisecancellation using PNC devices. There may be as many PNC devices asthere are independent data streams input into the transmitter. The PNCdevices are configured to cancel the effects of laser phase noise andany random phase shift introduced by the quantum channel. According toaspects of the present invention, each PNC device includes two squareoperators, one addition operator, a digital DC cancellation block and alow pass filtering block. Squaring in-phase and quadrature channels ofthe optical carrier cancels the effects of laser phase noise and anyrandom phase shifts introduced by the quantum channel, thus reducingbit-rate error. Accordingly, the original independent data streams maybe estimated with low bit-rate error in a highly secure fashion.

After that information reconciliation, based on systematic LDPC coding,is performed in similar fashion as already proposed for QKDapplications. To distill from the generated key a smaller set of bitswhose correlation with Eve's string falls below the desired threshold,the privacy amplification is performed with the help of the universalhash functions.

Another way to enable unconditional security is to employ the microwaveillumination approach, in which we can entangle mm-wave/THz/RF wave andoptical beam, so that through FL-QKD approach we can achieve multi-Gb/ssecure key rates over mm-wave/THz/RF links. In this scenario, the weakoptical beam is used to monitor Eve's intrusion, while mm-wave/THz/RFlink is used for raw-key transmission.

The foregoing is to be understood as being in every respect illustrativeand exemplary, but not restrictive, and the scope of the inventiondisclosed herein is not to be determined from the Detailed Description,but rather from the claims as interpreted according to the full breadthpermitted by the patent laws. It is to be understood that theembodiments shown and described herein are only illustrative of theprinciples of the present invention and that those skilled in the artmay implement various modifications without departing from the scope andspirit of the invention. Those skilled in the art could implementvarious other feature combinations without departing from the scope andspirit of the invention. Having thus described aspects of the invention,with the details and particularity required by the patent laws, what isclaimed and desired protected by Letters Patent is set forth in theappended claims.

What is claimed is:
 1. A method for quantum key distribution usingorbital angular momentum (OAM)-modes-enabled secure multidimensionalcoded modulation, comprising: modulating, at a transmitter, a pluralityof sequences, each of the plurality of sequences including at least oneof a plurality of symbols of a raw key, to generate a plurality ofsubcarriers corresponding to the plurality of sequences; subcarriermultiplexing the plurality of subcarriers into at least one electricalcarrier signal; optically modulating the at least one electrical carriersignal, via electro-optical modulation with an electro-opticalmodulator, into at least one optical carrier generated by an opticalsource, the electro-optical modulation including; imposing each of theat least one optical carrier on a pre-determined optical OAM mode, usingan optical OAM multiplexer configured to shift an azimuthal phase termof the transmitter corresponding to each of the pre-determined opticalOAM modes, to produce an optical OAM supercarrier containing each of theat least one optical carriers in a corresponding orthogonal OAM mode;attenuating the optical OAM supercarrier down to a shot noise levelrange with an optical attenuator; communicating the optical OAMsupercarrier across a quantum optical wireless communication channel;demultiplexing the optical OAM supercarrier, at a receiver, to extractprojections corresponding to at least one estimated optical carrier byshifting an azimuthal phase term of the receiver corresponding to eachof the pre-determine optical OAM modes; performing optical-to-electricalconversion on the at least one estimated optical carrier with thecoherent optical detector using an OAM projected signal, and signal froma local oscillator to generate at least one estimated electrical carriersignal; subcarrier demultiplexing each of the at least one estimatedelectrical carrier signal into a plurality of estimated subcarriers;phase noise cancelling, at a phase noise cancellation (PNC) stage, eachof the plurality of subcarriers to remove laser phase noise and randomphase shifts from the plurality of estimated subcarriers; anddemodulating the plurality of estimated subcarriers to extract aplurality of corresponding estimated symbol constellation pointscorresponding to the raw key.
 2. The method as recited in claim 1,wherein modulating the plurality of sequences includes: modulating eachof the symbols to impose each of the symbols onto a modulatedsubcarrier; and subcarrier multiplexing the modulated subcarriers toform the subcarrier multiplexed signal.
 3. The method as recited inclaim 1, wherein modulating the plurality of sequences includesmultidimensional modulation with a plurality of pulse shapers employingmutually orthogonal impulse responses derived from multiple orthogonalbasis functions including Slepian sequences to impose each of theplurality of sequences on multiple mutually orthogonal impulse responsesand form a corresponding multidimensional signal to be imposed on acorresponding subcarrier.
 4. The method as recited in claim 1, whereinmodulating the plurality of sequences includes performing quadratureamplitude modulation (QAM) to impose the plurality of sequences on anin-phase subcarrier and a quadrature subcarrier corresponding to theplurality of subcarriers such that the at least one electrical carriersignal includes a radio frequency (RF) subcarrier.
 5. The method asrecited in claim 1, wherein each of the plurality of sequences includesa symbol of the raw key generated with an arbitrary waveform generator(AWG).
 6. The method as recited in claim 1, wherein the optical sourceincludes one of a transmit laser diode or an amplified spontaneousemission (ASE) noise source.
 7. The method as recited in claim 1,wherein the optical OAM multiplexer includes at least one of a grating,computer generating hologram, or a spiral phase shifter configured toshift an azimuthal phase term of the optical carrier according to thepre-determined optical OAM mode.
 8. The method as recited in claim 1,wherein the balanced coherent detection includes: detecting amultidimensional signal carried by a given subcarrier imposed on a givenOAM mode by combining in an optical hybrid, a complex-conjugate OAMprojection and local oscillator laser signal; and determining adifference between photocurrents, using two photodetectors of thebalanced coherent detector, the difference corresponding to an estimatedelectrical multidimensional signal carried on a given subcarrier.
 9. Themethod as recited in claim 1, wherein the PNC stage includes: two squareoperations; one addition operation; a digital direct currentcancellation; and a low-pass filtering operation.
 10. The method asrecited in claim 1, further including reverse reconciliation usingsystematic low-density parity-check (LDPC) coding on the estimatedsymbol constellation points for continuous-variable quantum keydistribution for unconditional security.
 11. The method as recited inclaim 1, further including a flood-light quantum key distribution(FL-QKD) scheme employing microwave illumination.
 12. A transmitter forquantum key distribution using orbital angular momentum(OAM)-modes-enabled secure multidimensional coded modulation,comprising: at least one multidimensional modulation system including asubcarrier multiplexing system configured to multiplex a plurality ofmultidimensional signals, each of the plurality of multidimensionalsignals including at least one of a plurality of sequences of a raw key,to generate a plurality of subcarriers corresponding to the plurality ofsequences, and multiplex the plurality of subcarriers into at least oneelectrical carrier signal; an electro-optical modulator configured tomodulate the at least one electrical carrier signal via electro-opticalmodulation, into at least one optical carrier generated by an opticalsource, the electro-optical modulation including; imposing each of theat least one optical carrier on a pre-determined optical OAM mode, usingan optical OAM multiplexer including computer generated holograms, toproduce an optical OAM supercarrier containing each of the at least oneoptical carriers in a corresponding orthogonal OAM mode; and an opticalattenuator configured to attenuate the optical OAM supercarrier down toa shot noise level range and transmit the attenuated OAM supercarrierover a quantum channel.
 13. The transmitter as in claim 12, wherein eachmultidimensional modulation system is configured to modulate theplurality of sequences, including: modulating each of the sequences toimpose each of the sequences into a multidimensional space onto amultidimensionally modulated subcarrier; and subcarrier multiplexing themultidimensionally modulated subcarriers to form the at least oneelectrical carrier signal, including a subcarrier multiplexed RF signalused as an input to OAM multiplexer.
 14. The transmitter as recited inclaim 12, wherein the multidimensional modulation system includes aplurality of pulse shapers configured to modulate at least one sequence,wherein pulse shapers are implemented as filters employing mutuallyorthogonal impulse responses derived from multiple orthogonal basisfunctions including Slepian sequences to impose one or more sequences onmultiple mutually orthogonal impulse responses and form correspondingsubcarriers of the plurality of subcarriers.
 15. The transmitter asrecited in claim 12, wherein at least one multidimensional modulationsystem is configured to perform quadrature amplitude modulation (QAM) asmultidimensional signaling to impose at least one data sequence on anin-phase channel and a quadrature channel of a given subcarrier.
 16. Thetransmitter as recited in claim 12, wherein the optical OAM multiplexerincludes at least one azimuthal phase shifting device, each includingone of a grating, a computer generated hologram, or a spiral phaseshifter configured to shift an azimuthal phase term of the opticalcarrier according to the pre-determined optical OAM mode.
 17. A receiverfor quantum key distribution using orbital angular momentum(OAM)-modes-enabled secure multidimensional coded modulation,comprising: an optical OAM demultiplexer configured to perform OAMdemultiplexing of an optical OAM supercarrier to extract projectionscorresponding to at least one estimated optical carrier usingcomplex-conjugate shifting of an azimuthal phase term of the receivercorresponding to pre-determined optical OAM modes; a coherent opticaldetector configured to combine, with an optical hybrid, the projectionswith a laser signal from a local oscillator, perform balancedphotodetection for optical-to-electrical conversion, to determine anoptically detected subcarrier multidimensional signal; a subcarrierdemultiplexer configured to subcarrier demultiplex the correspondingoptically detected subcarrier multidimensional signal into a pluralityof multidimensional subcarriers; at least one phase noise cancellation(PNC) device configured to phase noise cancel each of the plurality ofsubcarriers to remove laser phase noise and random phase shifts from theplurality of estimated subcarriers; and at least one multidimensionaldemodulator, each corresponding to one of the plurality of estimatedsubcarriers and configured to demodulate at least one estimated sequenceof symbol constellation points corresponding to the raw key.
 18. Thereceiver as recited in claim 17, wherein the balanced coherent detectorincludes; an optical hybrid configured to mix the received subcarriermultidimensional signal carried by a given OAM mode with a laser signalfrom a local oscillator laser; and a balanced detector composed of twophotodetectors in a balanced configuration and configured to determine adifference between photocurrents from the optical hybrid outputs. 19.The receiver as recited in claim 17, wherein the at least one phasenoise cancellation device includes: two square operators; one additionoperator; a digital direct current cancellation block; and a low passfilter.
 20. The receiver as recited in claim 17, further includinglow-density parity-check (LDPC) decoders and an RF modulator for reversereconciliation using systematic low-density parity-check (LDPC) codingon the estimated symbol constellation points for continuous-variablequantum key distribution for unconditional security.